A fraction is always less than 1. E.g. 1/2, 2/5 etc.
Rational numbers can be fractions or also greater than 1. E.g. 7/3, 1/6 etc.
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Fraction number - A fraction is a number that express a part of the whole number as the quotient of integers where the denominator is not zero , another way to say that a fraction is a division expression where both dividend and divisor are integers and divisor is not zero.
Rational number - A rational number is a number that can be expressed as a quotient of integers or as a repeating or terminating decimal . Every fraction fit the first part of the definition , therefore every fraction is a rational number but not every rational number is a fraction.
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There is a huge difference between a fraction and a rational number. The concept of “fractional number” and “rational numbers” are closely related but are different in various aspects. It should be noted that “a fractional number is always a rational number but a rational number may or may not be a fractional number”.
Fraction and Rational Number Differences:
The difference in Definition: A fraction is any number of the form a/b where both “a” and “b” are whole numbers and b≠0. On the other hand, a rational number is a number which is in the form of p/q where both “p” and “q” are integers and q≠0.
Thus, a fraction is written in the form of a/b, where n is not 0 and m & n are whole (or natural numbers). For example, 12/23, 10/32, 12/10, 4/21. A rational number can also be written in the form of a/b, where b is not 0 and a & b are integers. For example, 15/7, -18/13, 3/-7, -6/-12. In general, rational numbers are denoted as p/q.
Why Every Fraction is a Rational Number but not Vice Versa?
All fractions can be termed as rational numbers, however, all rational numbers cannot be termed as fractions. Only those rational numbers in which ‘p’ and ‘q’ are positive integers are termed as fractions. Let a/b be any fraction. Now, a and b are natural numbers. Since all natural numbers are also integers, a and b are also integers. Thus, the fraction a/b is the quotient of 2 integers such that m ≠ 0. Hence, a/b is a rational number. One of the examples in which a number is a rational number but not a fraction is:
- Consider the fraction 12/-32. It is a rational number but not a fraction because its denominator (n) is not a natural number.
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